how to make star-shaped circle into a regular circle plane
I'd try to use something like rectangles instead of single N-gon. Like this:


Just delete face only, select the outer edge, press E to extrude, right click to cancel moving, S to scale almost to the center. then use Ctrl+R to add few edge loops, and fill the center. It will subdivide more consistently. And fix duplicating faces (flickering ones) to avoid problems on rendering.